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Seats for Mathematics, Science and arts in a school are in the ratio 5:7:8. There is a proposal to increase these seats by X%, Y% and Z% respectively. And the ratio of increased seats is 2:3:4, which of the following is true?
  • a)
    X = 50; Z = 40
  • b)
    Y = 40; Z = 50
  • c)
    X = 40; Z = 75
  • d)
    Y = 50; X = 75
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Seats for Mathematics, Science and arts in a school are in the ratio 5...
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)
i.e., 7x, 21x/2 and 14x
Required ratio = 7x:21x/2:14x
= 14x : 21x : 28x = 2:3:4
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Most Upvoted Answer
Seats for Mathematics, Science and arts in a school are in the ratio 5...
Answer – C.X = 40; Z = 75 Explanation : Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)
i.e., (140/100 * 5x), (150/100 * 7x) and (175/100 * 8x)
i.e., 7x, 21x/2 and 14x
Required ratio = 7x : 21x/2 : 14x
= 14x : 21x : 28x
= 2 : 3 : 4
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Community Answer
Seats for Mathematics, Science and arts in a school are in the ratio 5...
Given:
Ratio of seats for Mathematics, Science and Arts = 5:7:8
Ratio of increased seats = 2:3:4

To find:
The percentage increase in each category of seats.

Solution:
Let the common ratio between the initial number of seats and the increased number of seats be k.
Then, the initial number of seats for Mathematics, Science, and Arts will be 5k, 7k, and 8k respectively.
The increased number of seats for Mathematics, Science, and Arts will be 2k, 3k, and 4k respectively.

According to the question, the ratio of increased seats is 2:3:4.
2k:3k:4k can also be written as 2/9:3/9:4/9

Therefore, we can write:
2/9 = (5k + X% of 5k)/(2k)
3/9 = (7k + Y% of 7k)/(3k)
4/9 = (8k + Z% of 8k)/(4k)

Simplifying the above equations, we get:
X/10 = 1/9
Y/21 = 1/9
Z/8 = 1/9

Therefore, X = 40, Y = 21 and Z = 45.

Hence, the correct option is (C) X = 40, Z = 45.
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Seats for Mathematics, Science and arts in a school are in the ratio 5:7:8. There is a proposal to increase these seats by X%, Y% and Z% respectively. And the ratio of increased seats is 2:3:4, which of the following is true?a)X = 50; Z = 40b)Y = 40; Z = 50c)X = 40; Z = 75d)Y = 50; X = 75e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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